Site upgrade insisting on database upgrade after manual db upgrade

From your post, I presume you saw this message:

If so, the upgrade script still detects that you have PG 13 installed, which implies the old data directory is still being mounted in the container. Assuming the upgrade was successful, it’s possible the directories were not renamed correctly.

Keep in mind that launcher also checks for available disk space, but that returns a different message.

If you’re still stuck, share your sanitized app.yml file, all the commands you ran for the manual upgrade and their outputs, and the full output from the rebuild.